41st International Mathematical Olympiad
... fact that the smallest blue is k. This implies that k can only be 100. Since (i − 1) + 100 = i + 99, we see that 99 is white. We now show that 1 is red, 100 is blue, all the others are white. If t > 1 were red, then in view of t + 99 = (t − 1) + 100, t − 1 should be blue, but the smallest blue is 10 ...
... fact that the smallest blue is k. This implies that k can only be 100. Since (i − 1) + 100 = i + 99, we see that 99 is white. We now show that 1 is red, 100 is blue, all the others are white. If t > 1 were red, then in view of t + 99 = (t − 1) + 100, t − 1 should be blue, but the smallest blue is 10 ...
Sample Paper2
... b) q: For you to get an grade A, it is necessary and sufficient that you do all the homework regularly. c) r: If a quadrilateral is equiangular,then it is a rectangle and if a quadrilateral is a rectangle ,then it is equiangular. 18 A letter is chosen at random from the word “ASSASSINATION”. Find th ...
... b) q: For you to get an grade A, it is necessary and sufficient that you do all the homework regularly. c) r: If a quadrilateral is equiangular,then it is a rectangle and if a quadrilateral is a rectangle ,then it is equiangular. 18 A letter is chosen at random from the word “ASSASSINATION”. Find th ...
Solutions
... Note: The numbers used in the question varied from exam to exam, so your exam might have a different numerical answer than the one given below. 1. (3 pts) Sixteen people are to be seated at two circular tables, one seats 10 people and the other seats 6. How many different seating arrangements are po ...
... Note: The numbers used in the question varied from exam to exam, so your exam might have a different numerical answer than the one given below. 1. (3 pts) Sixteen people are to be seated at two circular tables, one seats 10 people and the other seats 6. How many different seating arrangements are po ...
Always a good review of all functions
... Identify the number of turns and model a situation using different degree polynomials. ...
... Identify the number of turns and model a situation using different degree polynomials. ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.